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Mirrors > Home > MPE Home > Th. List > mircom | Structured version Visualization version Unicode version |
Description: Variation on mirmir 25557. (Contributed by Thierry Arnoux, 10-Nov-2019.) |
Ref | Expression |
---|---|
mirval.p | |
mirval.d | |
mirval.i | Itv |
mirval.l | LineG |
mirval.s | pInvG |
mirval.g | TarskiG |
mirval.a | |
mirfv.m | |
mirmir.b | |
mircom.1 |
Ref | Expression |
---|---|
mircom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mircom.1 | . . 3 | |
2 | 1 | fveq2d 6195 | . 2 |
3 | mirval.p | . . 3 | |
4 | mirval.d | . . 3 | |
5 | mirval.i | . . 3 Itv | |
6 | mirval.l | . . 3 LineG | |
7 | mirval.s | . . 3 pInvG | |
8 | mirval.g | . . 3 TarskiG | |
9 | mirval.a | . . 3 | |
10 | mirfv.m | . . 3 | |
11 | mirmir.b | . . 3 | |
12 | 3, 4, 5, 6, 7, 8, 9, 10, 11 | mirmir 25557 | . 2 |
13 | 2, 12 | eqtr3d 2658 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wcel 1990 cfv 5888 cbs 15857 cds 15950 TarskiGcstrkg 25329 Itvcitv 25335 LineGclng 25336 pInvGcmir 25547 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rmo 2920 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-riota 6611 df-ov 6653 df-trkgc 25347 df-trkgb 25348 df-trkgcb 25349 df-trkg 25352 df-mir 25548 |
This theorem is referenced by: miduniq 25580 colperpexlem3 25624 mideulem2 25626 midex 25629 opphllem1 25639 opphllem2 25640 opphllem3 25641 opphllem5 25643 opphllem6 25644 trgcopyeulem 25697 |
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